Wireless spectrum is a valuable and scarce resource that currently suffers from under-use because of the dominant paradigm of exclusive-use licensing. We propose the SATYA auction (Sanskrit for truth), which allows short-term leases to be auctioned and supports diverse bidder types, including those willing to share access and those who require exclusive-use access. Thus, unlike unlicensed spectrum such as Wi-Fi, which can be shared by any device, and exclusive-use licensed spectrum, where sharing is precluded, SATYA improves efficiency through supporting sharing alongside quality-of-service protections. The auction is designed to be scalable, and also strategy proof, so that simple bidding protocols are optimal. The primary challenge is to handle the externalities created by allocating shared-use alongside exclusive-use bidders. Using realistic Longley-Rice based propagation modeling and data from the FCC’s CDBS database, we conduct extensive simulations that demonstrate SATYA’s ability to handle heterogeneous bidders involving different transmit powers and spectrum needs.